Despite offering a solution to several fundamental and conceptual problems of the standard big bang cosmology,
including the flatness, horizon, and exotic-relic problems, the cosmic inflation in the early universe
also provides a mechanism to produce density perturbations and primordial gravitational waves (PGWs) [1]}, [2]}, [3]}. The latter arise from quantum fluctuations of spacetimes and
produce not only a temperature anisotropy, but also polarizations in the cosmic microwave background (CMB), a smoking gun of PGWs.
However, the inflationary paradigm is incomplete without the knowledge of key elements from quantum gravity. First, it is well-known that the cosmic inflation is sensitive to the ultraviolet (UV) physics, and its successes are tightly contingent on the understanding of this UV physics [4]}, [5]}, [6]}.
In particular, if the inflationary phase lasts somewhat longer than the minimal period required to solve the above mentioned problems, the length scales we observe today will originate from modes that are smaller
than the Planck length during inflation [4]}. Then, the treatment of the underlying quantum field theory on a classical spacetime becomes questionable, as now the quantum geometric effects are expected to be large, and the space and time cannot be treated classically any more.
This is often referred to as the trans-Planckian problem of cosmological fluctuations It has been conjectured using models in string theory that the
trans-Planckian problem might never arise [8]}, which results on severe constraints on various cosmological models (See [9]}, [10]} for more details)..
